Harry Soodak

A geometric theory of rapidly spinning tops, tippe tops, and footballs

A perturbative geometric theory of rapidly spinning tops is presented and applied to gyroscopes supported against gravity at a fixed point, tippe tops with sliding friction, the motion of a well-thrown football pass, and the effect of spin-drag torques. The theory provides a conceptually simple and formally straightforward analysis of the smoothed variation of the angular momentum vector, and of the angle between it and the symmetry axis.

Wakes and waves in N dimensions

An impulsive point excitation in a linear, nondispersive wave medium can produce an after‐signal, which has been called a ‘‘wake’’ in the mathematical physics literature. Relations are derived between such wakes and the dimensionality of the space by regarding a point source in space of dimensionality N−2 as a line source in N−1 dimensions and as a plane source in N dimensions. The ‘‘magic’’ of one and three dimensions is discussed from a new point of view.

Perturbation analysis of rolling friction on a turntable

The effect of rolling friction on the motion of a ball rolling on a uniformly spinning horizontal turntable is evaluated by a first‐order perturbation approach, in which the unperturbed trajectories are the circular gyrations of the rolling ball in the absence of rolling friction. The analysis provides qualitative and quantitative understanding of the effect of rolling friction by itself and in combination with other ‘‘perturbations,’’ such as a tilt of the turntable.

Propagation of a Feynman error on real and inertial forces in rotating systems

Serious errors and misleading statements concerning real and inertial forces in rotating coordinate systems in The Feynman Lectures on Physics are pointed out and corrected.

Resolution analysis of gyroscopic motion

Two ideas, one kinematic and one dynamic, provide new insight into some of the amazing aspects of gyroscopic motion. The dynamic idea is to resolve the motion of the gyroscope in every short time interval as a superposition of its torque‐free motion and its torque‐induced motion. The kinematic idea is to directly track the motion of the symmetry axis.

Dynamic interpretation of Maxwell’s equations

Conventional discussions of Maxwell’s equations in free space have for many years taken a historical approach starting with electrostatics and magnetostatics, and have taught us that the sources of E are electric charge and Ḃ, and the sources of B are electric current and Ė. However, a direct dynamic reading of Maxwell’s differential equations leads unquestionably to the surprisingly different conclusions that the sources of E are electric current and curl B, and the single source of B is curl E. In this dynamic reading of Maxwell’s equations, electric field is generated locally by electric current, and fields propagate away from the current source by the dual mechanisms of curl E generating B locally and curl B generating E locally.

Ball moving on stationary or rotating horizontal surface

Interesting new results are added to the already amazing list of unexpected motions of balls moving on stationary or rotating surfaces. New and old results are discussed in a unified manner.

Dropped objects and other motions relative to the noninertial earth

Earth is a noninertial frame of reference due to its spin and its orbital free-fall acceleration in the gravity fields of the sun, moon, and other external attractors. Three particularly interesting aspects of motion relative to the earth are discussed: (a) the effect of the sun and the moon and other external gravitational attractors; (b) the Foucault pendulum at middle latitudes; (c) the venerable and surprising problem of the deviation of the path of a dropped object away from the plumb line. A selective review of the twentieth century physics literature on motion relative to the earth demonstrates that errors and omissions abound. A fourth example is also presented, the interesting textbook problem of the free motion of a particle on a frictionless horizontal plane, as a simple illustration of carelessly incorrect treatment in much of the literature.

Jack and the skyhook: The beanstalk revisited

The ’’skyhook’’ principle is discussed and applied to a uniform rope (Jack’s beanstalk) hanging from a point in the sky. The time for a transverse disturbances to travel from one end of the rope to the other (and back) is calculated.